HI 6326 Session 1

Overview:

  1. Lecture 1: Complex Numbers, Convolution, Fourier Transform (PDF file)
  2. Homework Assignment

Resources and Assignments:


Homework Assignment

Due at session 2. Hand in the written solutions at the beginning of class.

Problem 1: Convolution

Using the following diagram, explain the 2D convolution operation in your own words. Is this the first way (class notes slide number 20) or second way (class notes slide number 28) to compute the convolution?



Then, solve the 2D convolution problem in the class notes (slide number 30).

Problem 2: Fourier Transform

Using pencil and paper, compute the 1D Fourier Transform F(s) of the Gaussian: f(x) = exp (-π x2). Hint: In the FT equation, use a new integration variable by substituting y = x + i s, then express the exponent in terms of y2 and s2. Solve the integral over y, e.g. with a table of definite integrals.